When hydrogen is bonded to a highly electronegative atom (such as nitrogen, oxygen, and fluorine), the electrons are pulled more closely to the electronegative atom than to the hydrogen nucleus. This results in a partially positive charge on the hydrogen atom, which allows it to attract partially negative charged atoms on other molecules. This type of intermolecular force is called a hydrogen bond. 

Carbon and hydrogen have very similar electronegativities, so the electrons are equally shared. This makes methane a nonpolar molecule. As a result, it is incapable of hydrogen bonding with other molecules.

Hydrogen bonding only occurs when hydrogen is bound to either oxygen, nitrogen, or fluorine. Only these atoms form a bond with hydrogen polar enough so hydrogen bonding to occur.

 may participate in hydrogen bonding, which is one of the strongest intermolecular forces. Hydrogen bonding increases a substance's boiling point, and lowers its vapor pressure.

Differences in the physcal properties of substances is often due to differences in molecular structure.  Intermolecular forces can have profound effects on physical properties such as boiling point.  Substances with the same molecular formula can actually behave quite differently based on how the atoms in these substances are connected.  Hydrogen bonding is a strong intermolecular force that often leads to higher boiling points in substances that can hydrogen bond when compared to substances of similar molecular weights that cannot hydrogen bond with one another.  Thus the presence of hydrogen bonding in the unknown substance is the best answer.  

when a central atom of a molecule has 6 electron domains coming off of it (none of which are lone pairs of electrons), it is considered octahedral

The answer to this question can be determined by drawing a Lewis structure of the molecule. The S atom is central, with an O atom on each side. Adding in double bonds to each O atom and placing lone pairs on the O atoms give them each an octet, which leaves 2 more lone pairs of electrons to go on the S atom, creating a bent shape.

Molecules with three atoms around a central atom such as BF₃ are trigonal planar because electron repulsion is minimized by positioning the three attachments toward the corners of an equilateral triangle.

Multiple bonds, although they may be stronger, are not necessarily favored in a Lewis structure. It is dependent on the atoms involved. Thus, this is not a criterion used in determining a preferred Lewis structure.

In the reactant, , the carbon is bound to three hydrogens and one oxygen, and it has no lone pairs, so it has a tetrahedral geometry. In the product, , the carbon is bound to two hydrogens and one oxygen, so it must be double bonded to the oxygen in order to have a complete octet. Therefore, it has a trigonal planar geometry.

Ammonia exhibits a tetrahedral electron pair geometry. It has three bonded pairs (between nitrogen and each hydrogen), and one lone pair (on nitrogen). This combination forms a trigonal pyramidal molecular geometry.